हिंदी

State whether the following statement is True or False: ∫1+x2⋅xdx=13(1+x2)32+c

Advertisements
Advertisements

प्रश्न

State whether the following statement is True or False:

`int sqrt(1 + x^2) *x  "d"x = 1/3(1 + x^2)^(3/2) + "c"`

विकल्प

  • True

  • False

MCQ
सत्य या असत्य
Advertisements

उत्तर

True

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1.5: Integration - Q.3

संबंधित प्रश्न

Prove that `int_a^bf(x)dx=f(a+b-x)dx.` Hence evaluate : `int_a^bf(x)/(f(x)+f(a-b-x))dx`


Evaluate :

`int(sqrt(cotx)+sqrt(tanx))dx`


\[\int\sqrt{1 + x - 2 x^2} \text{ dx }\]

`int "dx"/(9"x"^2 + 1)= ______. `


 Prove that: `int "dx"/(sqrt("x"^2 +"a"^2)) = log  |"x" +sqrt("x"^2 +"a"^2) | + "c"`


Evaluate the following integrals : `intsqrt(1 + sin 5x).dx`


Integrate the following functions w.r.t. x : `((sin^-1 x)^(3/2))/(sqrt(1 - x^2)`


Integrate the following functions w.r.t. x : `(x.sec^2(x^2))/sqrt(tan^3(x^2)`


Integrate the following functions w.r.t. x : `(x^2 + 2)/((x^2 + 1)).a^(x + tan^-1x)`


Integrate the following functions w.r.t. x : `(2x + 1)sqrt(x + 2)`


Integrate the following functions w.r.t. x:

`(sinx cos^3x)/(1 + cos^2x)`


Choose the correct alternative from the following.

The value of `int "dx"/sqrt"1 - x"` is


`int sqrt(1 + "x"^2) "dx"` =


`int ("x + 2")/(2"x"^2 + 6"x" + 5)"dx" = "p" int (4"x" + 6)/(2"x"^2 + 6"x" + 5) "dx" + 1/2 int "dx"/(2"x"^2 + 6"x" + 5)`, then p = ?


Evaluate: If f '(x) = `sqrt"x"` and f(1) = 2, then find the value of f(x).


`int (2(cos^2 x - sin^2 x))/(cos^2 x + sin^2 x)` dx = ______________


`int  ("e"^x(x - 1))/(x^2)  "d"x` = ______ 


`int ("e"^(2x) + "e"^(-2x))/("e"^x)  "d"x`


`int cos^7 x  "d"x`


General solution of `(x + y)^2 ("d"y)/("d"x) = "a"^2, "a" ≠ 0` is ______. (c is arbitrary constant)


`int sec^6 x tan x   "d"x` = ______.


`int(7x - 2)^2dx = (7x -2)^3/21 + c`


Evaluate.

`int(5"x"^2 - 6"x" + 3)/(2"x" - 3)  "dx"`


Evaluate:

`int sin^2(x/2)dx`


Evaluate:

`int(cos 2x)/sinx dx`


Evaluate the following.

`int x^3/sqrt(1+x^4) dx`


Evaluate:

`int(5x^2-6x+3)/(2x-3)dx`


Evaluate.

`int (5x^2 -6x + 3)/(2x -3)dx`


Evaluate the following.

`int1/(x^2+4x-5)dx`


`int (x + 1)/(x(1 + xe^x)) dx` is equal to


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×